Python rs_tanh 예제들

예제 #1

파일: test_ring_series.py 프로젝트: LuckyStrikes1090/sympy

def test_tanh():
    R, x, y = ring('x, y', QQ)
    assert rs_tanh(x, x, 9) == -17/315*x**7 + 2/15*x**5 - 1/3*x**3 + x
    assert rs_tanh(x*y + x**2*y**3 , x, 9) == 4/3*x**8*y**11 - \
        17/45*x**8*y**9 + 4/3*x**7*y**9 - 17/315*x**7*y**7 - 1/3*x**6*y**9 + \
        2/3*x**6*y**7 - x**5*y**7 + 2/15*x**5*y**5 - x**4*y**5 - \
        1/3*x**3*y**3 + x**2*y**3 + x*y

예제 #2

파일: test_ring_series.py 프로젝트: vinothtronics/sympy

def test_tanh():
    R, x, y = ring('x, y', QQ)
    assert rs_tanh(x, x,
                   9) == -17 / 315 * x**7 + 2 / 15 * x**5 - 1 / 3 * x**3 + x
    assert rs_tanh(x*y + x**2*y**3 , x, 9) == 4/3*x**8*y**11 - \
        17/45*x**8*y**9 + 4/3*x**7*y**9 - 17/315*x**7*y**7 - 1/3*x**6*y**9 + \
        2/3*x**6*y**7 - x**5*y**7 + 2/15*x**5*y**5 - x**4*y**5 - \
        1/3*x**3*y**3 + x**2*y**3 + x*y

예제 #3

파일: test_ring_series.py 프로젝트: asmeurer/sympy

def test_tanh():
    R, x, y = ring('x, y', QQ)
    assert rs_tanh(x, x, 9)/x**5 == -S(17)/315*x**2 + S(2)/15 - S(1)/3*x**(-2) + x**(-4)
    assert rs_tanh(x*y + x**2*y**3, x, 9) == 4*x**8*y**11/3 - \
        17*x**8*y**9/45 + 4*x**7*y**9/3 - 17*x**7*y**7/315 - x**6*y**9/3 + \
        2*x**6*y**7/3 - x**5*y**7 + 2*x**5*y**5/15 - x**4*y**5 - \
        x**3*y**3/3 + x**2*y**3 + x*y

    # Constant term in series
    a = symbols('a')
    R, x, y = ring('x, y', EX)
    assert rs_tanh(x + a, x, 5) == EX(tanh(a)**5 - 5*tanh(a)**3/3 +
        2*tanh(a)/3)*x**4 + EX(-tanh(a)**4 + 4*tanh(a)**2/3 - QQ(1, 3))*x**3 + \
        EX(tanh(a)**3 - tanh(a))*x**2 + EX(-tanh(a)**2 + 1)*x + EX(tanh(a))

    p = rs_tanh(x + x**2*y + a, x, 4)
    assert (p.compose(x, 10)).compose(y, 5) == EX(-1000*tanh(a)**4 + \
        10100*tanh(a)**3 + 2470*tanh(a)**2/3 - 10099*tanh(a) + QQ(530, 3))

예제 #4

파일: test_ring_series.py 프로젝트: helpin/sympy

def test_tanh():
    R, x, y = ring('x, y', QQ)
    assert rs_tanh(x, x, 9) == -17/315*x**7 + 2/15*x**5 - 1/3*x**3 + x
    assert rs_tanh(x*y + x**2*y**3 , x, 9) == 4/3*x**8*y**11 - \
        17/45*x**8*y**9 + 4/3*x**7*y**9 - 17/315*x**7*y**7 - 1/3*x**6*y**9 + \
        2/3*x**6*y**7 - x**5*y**7 + 2/15*x**5*y**5 - x**4*y**5 - \
        1/3*x**3*y**3 + x**2*y**3 + x*y

    # Constant term in series
    a = symbols('a')
    R, x, y = ring('x, y', EX)
    assert rs_tanh(x + a, x, 5) == EX(tanh(a)**5 - 5*tanh(a)**3/3 + \
        2*tanh(a)/3)*x**4 + EX(-tanh(a)**4 + 4*tanh(a)**2/3 - QQ(1, 3))*x**3 + \
        EX(tanh(a)**3 - tanh(a))*x**2 + EX(-tanh(a)**2 + 1)*x + EX(tanh(a))

    p = rs_tanh(x + x**2*y + a, x, 4)
    assert (p.compose(x, 10)).compose(y, 5) == EX(-1000*tanh(a)**4 + \
        10100*tanh(a)**3 + 2470*tanh(a)**2/3 - 10099*tanh(a) + QQ(530, 3))

예제 #5

파일: test_ring_series.py 프로젝트: z-campbell/sympy

def test_tanh():
    R, x, y = ring('x, y', QQ)
    assert rs_tanh(x, x, 9) == -17 * x**7 / 315 + 2 * x**5 / 15 - x**3 / 3 + x
    assert rs_tanh(x*y + x**2*y**3 , x, 9) == 4*x**8*y**11/3 - \
        17*x**8*y**9/45 + 4*x**7*y**9/3 - 17*x**7*y**7/315 - x**6*y**9/3 + \
        2*x**6*y**7/3 - x**5*y**7 + 2*x**5*y**5/15 - x**4*y**5 - \
        x**3*y**3/3 + x**2*y**3 + x*y

    # Constant term in series
    a = symbols('a')
    R, x, y = ring('x, y', EX)
    assert rs_tanh(x + a, x, 5) == EX(tanh(a)**5 - 5*tanh(a)**3/3 + \
        2*tanh(a)/3)*x**4 + EX(-tanh(a)**4 + 4*tanh(a)**2/3 - QQ(1, 3))*x**3 + \
        EX(tanh(a)**3 - tanh(a))*x**2 + EX(-tanh(a)**2 + 1)*x + EX(tanh(a))

    p = rs_tanh(x + x**2 * y + a, x, 4)
    assert (p.compose(x, 10)).compose(y, 5) == EX(-1000*tanh(a)**4 + \
        10100*tanh(a)**3 + 2470*tanh(a)**2/3 - 10099*tanh(a) + QQ(530, 3))

예제 #6

def test_tanh():
    R, x, y = ring("x, y", QQ)
    assert rs_tanh(x, x, 9) / x**5 == Rational(-17, 315) * x**2 + Rational(
        2, 15) - Rational(1, 3) * x**(-2) + x**(-4)
    assert (rs_tanh(x * y + x**2 * y**3, x,
                    9) == 4 * x**8 * y**11 / 3 - 17 * x**8 * y**9 / 45 +
            4 * x**7 * y**9 / 3 - 17 * x**7 * y**7 / 315 - x**6 * y**9 / 3 +
            2 * x**6 * y**7 / 3 - x**5 * y**7 + 2 * x**5 * y**5 / 15 -
            x**4 * y**5 - x**3 * y**3 / 3 + x**2 * y**3 + x * y)

    # Constant term in series
    a = symbols("a")
    R, x, y = ring("x, y", EX)
    assert rs_tanh(
        x + a, x, 5
    ) == EX(tanh(a)**5 - 5 * tanh(a)**3 / 3 + 2 * tanh(a) / 3) * x**4 + EX(
        -tanh(a)**4 + 4 * tanh(a)**2 / 3 - QQ(1, 3)) * x**3 + EX(
            tanh(a)**3 - tanh(a)) * x**2 + EX(-tanh(a)**2 + 1) * x + EX(
                tanh(a))

    p = rs_tanh(x + x**2 * y + a, x, 4)
    assert (p.compose(x, 10)).compose(
        y, 5) == EX(-1000 * tanh(a)**4 + 10100 * tanh(a)**3 +
                    2470 * tanh(a)**2 / 3 - 10099 * tanh(a) + QQ(530, 3))

예제 #7

파일: test_ring_series.py 프로젝트: mayou36/sympy

def test_puiseux():
    R, x, y = ring('x, y', QQ)
    p = x**QQ(2, 5) + x**QQ(2, 3) + x

    r = rs_series_inversion(p, x, 1)
    r1 = -x**QQ(14,15) + x**QQ(4,5) - 3*x**QQ(11,15) + x**QQ(2,3) + \
        2*x**QQ(7,15) - x**QQ(2,5) - x**QQ(1,5) + x**QQ(2,15) - x**QQ(-2,15) \
        + x**QQ(-2,5)
    assert r == r1

    r = rs_nth_root(1 + p, 3, x, 1)
    assert r == -x**QQ(4, 5) / 9 + x**QQ(2, 3) / 3 + x**QQ(2, 5) / 3 + 1

    r = rs_log(1 + p, x, 1)
    assert r == -x**QQ(4, 5) / 2 + x**QQ(2, 3) + x**QQ(2, 5)

    r = rs_LambertW(p, x, 1)
    assert r == -x**QQ(4, 5) + x**QQ(2, 3) + x**QQ(2, 5)

    p1 = x + x**QQ(1, 5) * y
    r = rs_exp(p1, x, 1)
    assert r == x**QQ(4,5)*y**4/24 + x**QQ(3,5)*y**3/6 + x**QQ(2,5)*y**2/2 + \
        x**QQ(1,5)*y + 1

    r = rs_atan(p, x, 2)
    assert r ==  -x**QQ(9,5) - x**QQ(26,15) - x**QQ(22,15) - x**QQ(6,5)/3 + \
        x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_atan(p1, x, 2)
    assert r ==  x**QQ(9,5)*y**9/9 + x**QQ(9,5)*y**4 - x**QQ(7,5)*y**7/7 - \
        x**QQ(7,5)*y**2 + x*y**5/5 + x - x**QQ(3,5)*y**3/3 + x**QQ(1,5)*y

    r = rs_asin(p, x, 2)
    assert r == x**QQ(9,5)/2 + x**QQ(26,15)/2 + x**QQ(22,15)/2 + \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_cot(p, x, 1)
    assert r == -x**QQ(14,15) + x**QQ(4,5) - 3*x**QQ(11,15) + \
        2*x**QQ(2,3)/3 + 2*x**QQ(7,15) - 4*x**QQ(2,5)/3 - x**QQ(1,5) + \
        x**QQ(2,15) - x**QQ(-2,15) + x**QQ(-2,5)

    r = rs_cos_sin(p, x, 2)
    assert r[0] == x**QQ(28,15)/6 - x**QQ(5,3) + x**QQ(8,5)/24 - x**QQ(7,5) - \
        x**QQ(4,3)/2 - x**QQ(16,15) - x**QQ(4,5)/2 + 1
    assert r[1] == -x**QQ(9,5)/2 - x**QQ(26,15)/2 - x**QQ(22,15)/2 - \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_atanh(p, x, 2)
    assert r == x**QQ(9,5) + x**QQ(26,15) + x**QQ(22,15) + x**QQ(6,5)/3 + x + \
        x**QQ(2,3) + x**QQ(2,5)

    r = rs_sinh(p, x, 2)
    assert r == x**QQ(9,5)/2 + x**QQ(26,15)/2 + x**QQ(22,15)/2 + \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_cosh(p, x, 2)
    assert r == x**QQ(28,15)/6 + x**QQ(5,3) + x**QQ(8,5)/24 + x**QQ(7,5) + \
        x**QQ(4,3)/2 + x**QQ(16,15) + x**QQ(4,5)/2 + 1

    r = rs_tanh(p, x, 2)
    assert r == -x**QQ(9,5) - x**QQ(26,15) - x**QQ(22,15) - x**QQ(6,5)/3 + \
        x + x**QQ(2,3) + x**QQ(2,5)

예제 #8

파일: test_ring_series.py 프로젝트: asmeurer/sympy

def test_puiseux():
    R, x, y = ring('x, y', QQ)
    p = x**QQ(2,5) + x**QQ(2,3) + x

    r = rs_series_inversion(p, x, 1)
    r1 = -x**QQ(14,15) + x**QQ(4,5) - 3*x**QQ(11,15) + x**QQ(2,3) + \
        2*x**QQ(7,15) - x**QQ(2,5) - x**QQ(1,5) + x**QQ(2,15) - x**QQ(-2,15) \
        + x**QQ(-2,5)
    assert r == r1

    r = rs_nth_root(1 + p, 3, x, 1)
    assert r == -x**QQ(4,5)/9 + x**QQ(2,3)/3 + x**QQ(2,5)/3 + 1

    r = rs_log(1 + p, x, 1)
    assert r == -x**QQ(4,5)/2 + x**QQ(2,3) + x**QQ(2,5)

    r = rs_LambertW(p, x, 1)
    assert r == -x**QQ(4,5) + x**QQ(2,3) + x**QQ(2,5)

    p1 = x + x**QQ(1,5)*y
    r = rs_exp(p1, x, 1)
    assert r == x**QQ(4,5)*y**4/24 + x**QQ(3,5)*y**3/6 + x**QQ(2,5)*y**2/2 + \
        x**QQ(1,5)*y + 1

    r = rs_atan(p, x, 2)
    assert r ==  -x**QQ(9,5) - x**QQ(26,15) - x**QQ(22,15) - x**QQ(6,5)/3 + \
        x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_atan(p1, x, 2)
    assert r ==  x**QQ(9,5)*y**9/9 + x**QQ(9,5)*y**4 - x**QQ(7,5)*y**7/7 - \
        x**QQ(7,5)*y**2 + x*y**5/5 + x - x**QQ(3,5)*y**3/3 + x**QQ(1,5)*y

    r = rs_asin(p, x, 2)
    assert r == x**QQ(9,5)/2 + x**QQ(26,15)/2 + x**QQ(22,15)/2 + \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_cot(p, x, 1)
    assert r == -x**QQ(14,15) + x**QQ(4,5) - 3*x**QQ(11,15) + \
        2*x**QQ(2,3)/3 + 2*x**QQ(7,15) - 4*x**QQ(2,5)/3 - x**QQ(1,5) + \
        x**QQ(2,15) - x**QQ(-2,15) + x**QQ(-2,5)

    r = rs_cos_sin(p, x, 2)
    assert r[0] == x**QQ(28,15)/6 - x**QQ(5,3) + x**QQ(8,5)/24 - x**QQ(7,5) - \
        x**QQ(4,3)/2 - x**QQ(16,15) - x**QQ(4,5)/2 + 1
    assert r[1] == -x**QQ(9,5)/2 - x**QQ(26,15)/2 - x**QQ(22,15)/2 - \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_atanh(p, x, 2)
    assert r == x**QQ(9,5) + x**QQ(26,15) + x**QQ(22,15) + x**QQ(6,5)/3 + x + \
        x**QQ(2,3) + x**QQ(2,5)

    r = rs_sinh(p, x, 2)
    assert r == x**QQ(9,5)/2 + x**QQ(26,15)/2 + x**QQ(22,15)/2 + \
        x**QQ(6,5)/6 + x + x**QQ(2,3) + x**QQ(2,5)

    r = rs_cosh(p, x, 2)
    assert r == x**QQ(28,15)/6 + x**QQ(5,3) + x**QQ(8,5)/24 + x**QQ(7,5) + \
        x**QQ(4,3)/2 + x**QQ(16,15) + x**QQ(4,5)/2 + 1

    r = rs_tanh(p, x, 2)
    assert r == -x**QQ(9,5) - x**QQ(26,15) - x**QQ(22,15) - x**QQ(6,5)/3 + \
        x + x**QQ(2,3) + x**QQ(2,5)